MBSlib–An Efficient Multibody Systems Library for Kinematics and Dynamics Simulation, Optimization and Sensitivity Analysis

Wojtusch, Janis; Kunz, Jürgen; Stryk, Oskar von

doi:10.1109/lra.2016.2527830

Cited by 6 publications

(3 citation statements)

References 19 publications

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“…Instead, it relies on dynamic data structures, which introduces significant overhead and limits the usability of the library for hard real-time, multi-threaded and embedded applications. MBSlib [13] also provides Auto-Diff support and does so in a more rigorous manner. Yet, it also relies on dynamic data structures, limiting efficiency and potential embedded and control applications.…”

Section: Related Workmentioning

confidence: 99%

Automatic differentiation of rigid body dynamics for optimal control and estimation

et al. 2017

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Many algorithms for control, optimization and estimation in robotics depend on derivatives of the underlying system dynamics, e.g. to compute linearizations, sensitivities or gradient directions. However, we show that when dealing with Rigid Body Dynamics, these derivatives are difficult to derive analytically and to implement efficiently. To overcome this issue, we extend the modelling tool 'RobCoGen' to be compatible with Automatic Differentiation. Additionally, we propose how to automatically obtain the derivatives and generate highly efficient source code. We highlight the flexibility and performance of the approach in two application examples. First, we show a Trajectory Optimization example for the quadrupedal robot HyQ, which employs auto-differentiation on the dynamics including a contact model. Second, we present a hardware experiment in which a 6 DoF robotic arm avoids a randomly moving obstacle in a go-to task by fast, dynamic replanning. This paper is an extended version of [1].

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Section: Related Workmentioning

confidence: 99%

Automatic differentiation of rigid body dynamics for optimal control and estimation

et al. 2017

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“…showed that trajectory optimization of gait for a quadrupedal robot modeled with RobCoGen was five times faster with AD than with FD [27]. Other packages for robotic applications with modules supporting AD include Drake [28], Robotran [29], MBSlib [30], and Pinocchio [31]. Drake is a collection of tools that relies on Eigen [32] for linear algebra.…”

Section: Introductionmentioning

confidence: 99%

Algorithmic differentiation improves the computational efficiency of OpenSim-based trajectory optimization of human movement

et al. 2019

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Algorithmic differentiation (AD) is an alternative to finite differences (FD) for evaluating function derivatives. The primary aim of this study was to demonstrate the computational benefits of using AD instead of FD in OpenSim-based trajectory optimization of human movement. The secondary aim was to evaluate computational choices including different AD tools, different linear solvers, and the use of first-or second-order derivatives. First, we enabled the use of AD in OpenSim through a custom source code transformation tool and through the operator overloading tool ADOL-C. Second, we developed an interface between OpenSim and CasADi to solve trajectory optimization problems. Third, we evaluated computational choices through simulations of perturbed balance, two-dimensional predictive simulations of walking, and three-dimensional tracking simulations of walking. We performed all simulations using direct collocation and implicit differential equations. Using AD through our custom tool was between 1.8 ± 0.1 and 17.8 ± 4.9 times faster than using FD, and between 3.6 ± 0.3 and 12.3 ± 1.3 times faster than using AD through ADOL-C. The linear solver efficiency was problem-dependent and no solver was consistently more efficient. Using second-order derivatives was more efficient for balance simulations but less efficient for walking simulations. The walking simulations were physiologically realistic. These results highlight how the use of AD drastically decreases computational time of trajectory optimization problems as compared to more common FD. Overall, combining AD with direct collocation and implicit differential equations decreases the computational burden of trajectory optimization of human movement, which will facilitate their use for biomechanical applications requiring the use of detailed models of the musculoskeletal system. Algorithmic differentiation speeds up trajectory optimization of human movement PLOS ONE | https://doi.Fig 2.Flowchart depicting the optimal control framework. We developed two approaches (AD-ADOLC and AD-Recorder) to make an OpenSim function F and its forward (F fwd) and reverse (F rev) directional derivatives available within the CasADi environment for use by the NLP solver during the optimization. In the AD-ADOLC approach (top), ADOL-C's algorithms are used in a C++ code to provide F fwd and F rev. In the AD-Recorder approach (bottom), Recorder provides the expression graph of F as MATLAB source code from which CasADi's C-code generator generates C-code containing F, F fwd, and F rev. The AD-Recorder approach combines operator overloading, when generating the expression graph, and source code transformation, when processing the expression graph to generate C-code for F, F fwd, and F rev. In both approaches, the code comprising F, F fwd, and F rev is compiled as a Dynamic-link Library (DLL), which is imported as an external function within the CasADi environment. In our application, F represents the multi-body dynamics and is called when formulating the optimal control problem. The latte...

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“…Code derivation is possible (Wojtusch et al , 2016). It could be implemented for the dynamic simulation of power electronics.…”

Section: Introductionmentioning

confidence: 99%

Obtaining the most exact Jacobian of the time modelling of power electronics structures for gradient-based optimisations

Gerbaud

Diarra

Chazal

et al. 2022

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Purpose The paper aims to deal with the exact computation of the Jacobian of a time criteria from a numerical simulation of power electronics structures, for the sizing by gradient-based optimization algorithm. Design/methodology/approach Runge Kutta 44 is used to solve the state equations. The generic approach combines numerical and symbolic approaches. The modelling of the static converter is based on ideal switches. Findings The paper extends the state equations to derivate any state variable according a sizing parameter. The integral expressions used for some sizing performances (e.g. average or RMS values) mix symbolic and numerical approaches. Choices are made for the derivatives of the extrema of which the search is not a continuous process. The use of an object-oriented implementation allows to have generic formulation of some design performances. Research limitations/implications The paper aims to propose and to test formulations of sizing criteria and their gradients; so, the modelling of the study case is carried out manually. Due to generic modelling approach used for the power electronics, the model is not completely continuous. So, the derivatives according some parameters (e.g. switch controls) must be carried out by finite differences. However, as the global behaviour is continuous, it is not critical. Practical implications The proposed formulations can be easily applied on simple static converter applications. For applications with large state equations, it should be possible to use the basic model of switches used in simulation tools of power electronics. The solving process and the sizing criteria formulation (with their derivatives) are generic and can be instantiate for any study. Originality/value The approach proposes formulations giving a numerical sizing dynamic model with a Jacobian computed, if possible, by an exact derivation useful for optimization studies. The approach gives fast simulation and fast computation of the derivatives by combining numerical and analytical approaches.

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MBSlib–An Efficient Multibody Systems Library for Kinematics and Dynamics Simulation, Optimization and Sensitivity Analysis

Cited by 6 publications

References 19 publications

Automatic differentiation of rigid body dynamics for optimal control and estimation

Automatic differentiation of rigid body dynamics for optimal control and estimation

Algorithmic differentiation improves the computational efficiency of OpenSim-based trajectory optimization of human movement

Obtaining the most exact Jacobian of the time modelling of power electronics structures for gradient-based optimisations

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